The way I was taught, and the way I have made collages in the past was to position the pieces like you've shown, and then cut away the lower each print where the upper print overlaps so each piece fit right into each other on one final "layer". It is much cleaner than having prints sitting on top of each other, and there is no possibility for the edges to lift. I am a huge fan of rubber cement in collage applications.
If it were me, I would position and cut all the pieces, and then apply a thin coat of rubber cement to the back of each and then let them dry. Then take a second sheet of paper that will act as the carrier and coat it with rubber cement a little larger than the area of the pieces you are mounting and let that dry also. Adhere the largest piece to the carrier first—it will make a permanent bond as soon as the two dry rubber cement surfaces come in contact with each other so play with a few scraps first so you can get the feel for it. Then assemble and adhere the rest of the pieces to the carrier sheet. When it is finally assembled you just cut away the remaining support sheet and then you can mount that to the matboard however you like.